Abstract
The relationship between the generalized growth parameters of an entire harmonicfunction in space Rn, n ≥ 3, with the rate of its best harmonic polynomial approximation error and ratios of these errors of functions harmonic in the ball of radius R has been studied.
Highlights
The approximation of entire functions on compact sets was studied by Srivastava and Kumar [14,15] and obtained generalized growth parameters in terms of approximation and interpolation error
Similar studies have been done for harmonic functions
Harmonic functions can be expanded into series in spherical harmonics in space Rn, n ≥ 3 and in the adjoined Legendre polynomials in space R3
Summary
The approximation of entire functions on compact sets was studied by Srivastava and Kumar [14,15] and obtained generalized growth parameters in terms of approximation and interpolation error. The concept of type T (F ) and lower type t(F ) has been introduced when the entire functions have same nonzero finite order. An entire function of order ρ, 0 < ρ < ∞, is said to be of type T (F ) and lower type t(F ) if log M (r, F )
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